Kinetic Coefficients in the Boundary-Value Problem on the Slip of a Multiatomic Gas with Rotational Degrees of Freedom

The boundary-value problem on the slip of an inhomogeneous multiatomic gas along the spherical surface of small curvature is solved. For this purpose, a model kinetic equation that includes the rotational degrees of freedom of molecules is proposed. The solution is performed using the method of half-space moments. Gas-kinetic slip coefficients and jumps of macroscopic parameters of gas of the first and second order in the Knudsen number are obtained. These gas-kinetic coefficients are represented in the form of functions depending on the accommodation coefficient of tangential momentum, on the accommodation coefficients of the translational and rotational components of energy, and on the Prandtl number. For a number of multiatomic gases, calculations of the above-mentioned coefficients are performed.     

The Temperature Dependence of the Coefficients of Thermal and Isothermal Slip of a Diatomic Gas with Rotational Degrees of Freedom

A model kinetic equation is suggested for diatomic gases with rotational degrees of freedom of molecules. The free parameters of the model are related to Eucken's partial factors. This model is used to solve the problem on the slip of a diatomic gas along a plane surface. The coefficients of thermal and isothermal slip are obtained in the form of functions dependent on the transport coefficients and the frequency of inelastic collisions of gas molecules and, as a consequence, on the temperature.     

Analytical solution of the problem on thermal slip of second order for molecular gases

Results obtained using exact analytical methods in the problem on thermal slip of second order for molecular gases with allowance for the rotational degrees of freedom of molecules have been presented. Numerical calculations of the thermal-slip coefficient for a number of molecular gases have been carried out. The dependence of the velocity of thermal slip of second order of a molecular gas on the Prandtl number has been shown. The found value of the coefficient of thermal slip of second order theoretically confirms the existence of negative (in the direction of the temperature gradient) thermophoresis for molecular gases. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 3, pp. 190–194, May–June, 2006.     

The effect of inelastic collisions on the diatomic gas temperature jump in the vicinity of a solid surface

The problem on temperature jump in the vicinity of a solid surface is solved by the method of half-space moments using the previously suggested model kinetic equation which takes into account the rotational degrees of freedom of molecules of a diatomic gas. The temperature jump coefficient is obtained in the form of a function dependent on the coefficient of accommodation of tangential momentum, the coefficients of accommodation of translational and rotational components of energy, thermophysical parameters, and the frequency of inelastic collisions of gas molecules. The temperature jump coefficient is calculated for a number of diatomic gases. Graphs are given of the dependence of the temperature jump coefficient on the inelastic collision frequency and on the accommodation coefficients.     

基于并联机构中医推拿机器人机型研究

 在对中医推拿手法运动学研究的基础上，依据中医推拿手法运动学特征并结合并联机构的特点，提出基于并联机构中医推拿机器人机型及输出矩阵。对基于三平移三转动并联机构、三平移两转动并联机构、两平移三转动并联机构、两平移两转动并联机构、两平移一转动并联机构的中医推拿机器人进行了概念设计，并利用Pro/E软件构建出各机型虚拟样机。最后从动平台输出矩阵、控制解耦性、结构对称性、工作空间及转动能力等方面对各机型进行了分析总结。为各中医推拿机器人的实际应用提供了理论依据。     

力矩激励器功率输出特性

力矩激励器是一种新型传感器 ,用于研究结构声转动自由度的特性。本文利用互功率谱方法对力矩激励器的最大不失真力矩输出功率和相对应的输入电功率进行了测量 ,并计算了其电 力功率转换效率     

Heat and mass transfer of a multiatomic gas in a cylindrical capillary with arbitrary Knudsen numbers

Processes of heat and mass transfer of a multiatomic gas in a cylindrical channel of circular cross section with arbitrary Knudsen numbers are considered on the basis of a model kinetic equation, taking account of the excitation of rotational and vibrational degrees of freedom of the molecules.Notation Kn Knudsen number - f, f^tr total and translational Eucken factors - R_o capillary radius - m molecular mass - k Boltzmann's constant - n, T numerical density and temperature of gas - v_i i-th component of the molecular velocity - h_ij perturbation function - E_i ^(r), e_j ^(v) energy of the i-th rotational and j-th vibrational levels - E_o ^(r), E_o ^(v) equilibrium values of the rotational and vibrational energy - P_i ^(r), P_i ^(v) probability of rotational and vibrational states of energy E _i ^r and E _j ^v - , logarithmic pressure and temperature gradients - T_o mean gas temperature - R rarefaction parameter of gas - C _V ^r , C _V ^v contributions of rotational and vibrational degrees of freedom of the molecule to the specific heat at constant volume - U macroscopic gas velocity - q^(t), q^(r), q^(v) components of the heat flux density due to translational, rotational, and vibrational degrees of freedom of the molecules - P, pressure and dynamic viscosity of the gas - l free path length of molecules - up velocity of Poiseuille flow - u_T rate of thermal creep - cross-sectional area of capillary - I_n, I_q numerical and heat fluxes averaged over the channel cross section - universal index characterizing the thermomolecular pressure difference - ^t, ^r, ^v thermal conductivities due to translational, rotational, and vibrational degrees of freedom of the molecules - mass density of the gas - D_rr, D_vv diffusion coefficients of rotationally and vibrationally excited molecules among the unexcited molecules - Z_r rotational collisional number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 47, No. 1, pp. 71–82, July, 1984.     

Dynamic analysis and drilling degrees of freedom

Finite element methods for dynamic analysis employing elements with drilling degrees of freedom are presented. The formulation is based on a variational principle in which displacements and rotations are interpolated independently. The issue of zero masses corresponding to rotational degrees of freedom is addressed and techniques for defining consistent and lumped rotational mass matrices are presented.     

Investigation of nonequilibrium rf-discharge plasma in nitrogen using the method of wide-band CARS spectroscopy

The method of wide-band spectroscopy of coherent anti-Stokes Raman scattering of light (CARS) is used for the first time to investigate low-temperature inductive-capacitive radio-frequency discharge (rf-discharge) plasma in nitrogen at a pressure of 20 torr and specific power up to 3 W/cm³. A disturbance of thermodynamic equilibrium over internal degrees of freedom of nitrogen is observed in gas-discharge plasma. The function of distribution of molecules over vibrational levels v = 0–2 is described by the Treanor distribution, and that over rotational levels — by the Boltzmann distribution. Computer codes are developed for analyzing CARS spectra under conditions of disturbance of thermodynamic equilibrium over internal degrees of freedom of nitrogen molecules.     

A model for transport of diatomic molecules through elastic solids

Summary The distribution function of diatomic molecules, dissolved in a solid matrix subject to thermal elastic motion, was evaluated in closed form, assuming separability between the translational and rotational degrees of freedom of the solute molecules. The approach was applied to studying the transport of oxygen molecules through atomistic microstructures of atactic poly(vinylchloride) of ca. 40 Å at 318 K. The solubility coefficient was determined from the normalization constant of . The diffusion coefficient was evaluated from the long-term random walks of O₂ molecules on the network of local maxima of . Comparison with experimental data resulted in satisfactory agreement, indicating the viability of the approach.     

An assumed-stress hybrid 4-node shell element with drilling degrees of freedom

An assumed-stress hybrid/mixed 4-node quadrilateral shell element is introduced that alleviates most of the deficiencies associated with such elements. The formulation of the element is based on the assumed-stress hybrid/mixed method using the Hellinger-Reissner variational principle. The membrane part of the element has 12 degrees of freedom including rotational or ‘drilling’ degrees of freedom at the nodes. The bending part of the element also has 12 degrees of freedom. The bending part of the element uses the Reissner-Mindlin plate theory which takes into account the transverse shear contributions. The element formulation is derived from an 8-node isoparametric element by expressing the midside displacement degrees of freedom in terms of displacement and rotational degrees of freedom at corner nodes. The element passes the patch test, is nearly insensitive to mesh distortion, does not ‘lock’, possesses the desirable invariance properties, has no hidden spurious modes, and for the majority of test cases used in this paper produces more accurate results than the other elements employed herein for comparison.     

Simulation of tension fields with in-plane rotational degrees of freedom

This paper introduces a novel multigrid approach for the geometric non-linear simulation of tension fields on the basis of a three-node membrane finite element. The element possesses, in addition to the nodal displacement degrees of freedom, an in-plane rotational degree of freedom inside the element domain that controls the direction of the tension field. This rotational degree of freedom allows the enforcement of continuity and tension field boundary conditions on the basis of a coarser mesh with varying size.     

可倾瓦滑动轴承系统线性稳定性分析

提出可倾瓦轴承系统解析模型并对其进行线性稳定性分析。采用Newton-Raphson和pad assembly这两种方法,可获得系统完整的动力特性系数。基于这些动力特性系数,建立系统的运动微分方程并进行复特征值分析,易求得用来检验系统稳定性的轴瓦临界质量和系统阻尼比。结果表明:预负荷、转速及支点位置均对可倾瓦轴承系统的稳定性有着较大的影响,合理选取这些参数有助于提高系统的稳定临界值。     

Local ordering in dilute ortho-para-hydrogen mixtures at low temperatures

We report experimental observations of the local orientational ordering of ortho-H₂ molecules in dilute solid ortho-para mixtures for low temperatures. The results indicate a smooth, continuous freezing of the rotational degrees of freedom without any evidence for a distinct discontinuity in the temperature dependence of the local order parameters for the 37–600 mK temperature range.     

A finite element for the linear analysis of laminated circular plates

A new finite element for modeling axiysymmetric circular plates is developed. The element is based upon Mindlin's shear-deformable plate theory, and elements may be stacked on top of one another to model laminated plate by the addition of only rotational degrees of freedom for each lamina. The elements assure continuity of the displacements between the layers, but not continuity of the traction vectors. Neither interlaminar slip nor debonding between the layers is considered.

The plate element is more efficient at modeling laminated structures than conventional plate elements or solid elements because it accurately models the structure while keeping the degrees of freedom per element to a minimum. If one were to use solid elements to model a laminated circular plate, many more elements would have to be used in the model to avoid loss of accuracy due to a large aspect ratio. Each layer in the laminated plate is allowed an independent rotation: hence, the model gives more accurate results than classical lamination theory models. The new element is also immune from shear locking at least for radius-to-thickness ratios up to 500 without having to incorporate reduced numerical integration schemes. In fact, the element's stiffness matrix may be integrated in closed form: this is not possible for most plate elements in the literature.     

Dynamics of an elastic multibody chain: Part D—Modelling of joints

In the three previous papers in this series on the dynamics of a topological chain of arbitrary elastic bodies, rotational and translational displacements of arbitrary magnitude were allowed at all interbody joints. While this degree of generahty lends relevance withrespect to a diverse range of robotics applications, a careful specification of the displacement and force components at each joint becomes mandatory. In the present analysis, from one to six degrees of freedom are permitted at each joint, as reflected in the number of columns in its joint projection matrix. The special but practically important cases ofrotational (revolute) joints with one, two or three degrees of freedom are considered in detail, including physical interpretations for the coefficient matrices in the equations of motion. With robotics applications in mind, the many possibilities for sensors and actuators at the joints are catalogued and the four most important classes of ‘sensactor’ (a colocated sensor/actuator pair) are identified and their implications for the system equations presented.     

RxPzRy型2R1T部分解耦并联机构设计与分析

目的分析部分解耦的2R1T并联机构驱动副旋量特征,从而设计一类新型的部分解耦的RxPzRy型2R1T并联机构。方法基于完全解耦的并联机构的输入输出关系,将动平台角速度在定坐标系轴线方向的分量,变换为XYZ欧拉角角速度分量,得到角速度的完全解耦的分块雅可比矩阵,得到具有多个转动自由度机构的输出与输入部分解耦的关系。结果设计了一种新型部分解耦2R1T并联机构,分析表明该机构部分解耦。结论对于RxPzRy型2R1T并联机构在解耦设计时,使用旋量理论得到的关于角速度的雅克比矩阵不适用于具有多个转动自由度的并联机构完全解耦设计,使用文中提出的变换矩阵将其变换为关于欧拉角的角速度的雅克比矩阵,可以得到相应的对角矩阵,这种方法可以用来对具有多个转动自由度的并联机构完全解耦设计。     

Analytical Solution of a Nonhomogeneous Kinetic Equation with a Variable Frequency of Collisions

The problem of calculation of a correction to the coefficient of isothermal slip that is due to the wall curvature is solved. For this purpose we constructed the exact solution of a nonhomogeneous model kinetic Boltzmann equation with a collision operator in the form of the BGK model with the frequency of collisions proportional to the modulus of the intrinsic velocity of gas molecules. Comparison with the results obtained earlier is given.